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On Superluminal Particles and the Extended Relativity Theories

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Abstract

Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass \(\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }\) is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because the true physical mass still obeys M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. A Born’s Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 GeV, we find a value for the magnitude \(|\mathcal{M } | = 119.7\mbox{~MeV}\) that, coincidentally, is close to the mass of the muon m μ =105.7 MeV.

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Notes

  1. 1.

    The choice e=0,M≠0 is more appropriate for the scalar massive mesons.

References

  1. 1.

    Castro, C., Pavsic, M.: Prog. Phys. 1, 31 (2005)

  2. 2.

    Castro, C., Pavsic, M.: Phys. Lett. B 559, 74 (2003)

  3. 3.

    Castro, C., Pavsic, M.: Int. J. Theor. Phys. 42, 1693 (2003)

  4. 4.

    Castro, C.: Found. Phys. 35(6), 971 (2005)

  5. 5.

    Castro, C.: Prog. Phys. 1, 20 (2005)

  6. 6.

    Ansoldi, S., Aurilia, A., Spallucci, E.: Phys. Rev. D 56(4), 2532 (1997)

  7. 7.

    Ansoldi, S., Aurilia, A., Castro, C., Spallucci, E.: Phys. Rev. D 64, 026003 (2001)

  8. 8.

    Pezzaglia, W.: Dimensionally democratic calculus and principles of polydimensional physics. arXiv:gr-qc/9912025

  9. 9.

    Pezzaglia, W.: Physical applications of a generalized Clifford calculus (Papapetrou equations and metamorphic curvature). arXiv:gr-qc/9710027

  10. 10.

    Pezzaglia, W.: Polydimensional relativity, a classical generalization of the automorphism invariance principle. arXiv:gr-qc/9608052

  11. 11.

    Pavsic, M.: Found. Phys. 33, 1277 (2003)

  12. 12.

    Pavsic, M.: The Landscape of Theoretical Physics: A Global View, from Point Particles to the Brane World and Beyond, in Search of a Unifying Principle. Fundamental Theories of Physics, vol. 19. Kluwer Academic, Dordrecht (2001)

  13. 13.

    Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus. Reidel, Dordrecht (1984)

  14. 14.

    Doran, C., Lasenby, A.: Geometric Algebra for Physicists. Cambridge University Press, Cambridge (2003)

  15. 15.

    Adam, T., et al.: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam. arXiv:1109.4897

  16. 16.

    Recami, E.: Riv. Nuovo Cimento 9(6), 1 (1986)

  17. 17.

    Recami, E., Mignani, R.: Riv. Nuovo Cimento 4, 209 (1974). (Erratum 398)

  18. 18.

    E. Recami’s website: www.unibg.it/recami

  19. 19.

    Giannetto, E., Maccarrone, G., Migani, R., Recami, E.: Phys. Lett. B 178, 115 (1986)

  20. 20.

    Recami, E.: Found. Phys. 31(7), 1119 (2001)

  21. 21.

    Recami, E.: Multi-verses, micro-universes and elementary particles (hadrons). arXiv:physics/0505149

  22. 22.

    Rosen, N.: Found. Phys. 10, 673 (1980)

  23. 23.

    Isham, C., Salam, A., Strathdee, J.: Phys. Rev. D 3, 867 (1971)

  24. 24.

    Ne’eman, Y.: Hadron. J. 21, 255 (1998)

  25. 25.

    Salesi, G.: Int. J. Mod. Phys. A 28, 5103 (1997)

  26. 26.

    Faria-Rosa, M.A., Recami, E., Rodrigues, W.A. Jr.: Phys. Lett. B 173, 233 (1986). Phys. Lett. B 188, 511 (1987) (Erratum)

  27. 27.

    Rodrigues, W.A. Jr., Recami, E., Maia, A. Jr., Rosa, M.A.F.: Phys. Lett. B 220, 195 (1989)

  28. 28.

    Maia, A. Jr., Recami, E., Rodrigues, W.A. Jr., Faria-Rosa, M.A.: J. Math. Phys. 31, 502 (1990)

  29. 29.

    Maia, A. Jr., Recami, E., Rodrigues, W.A. Jr., Faria-Rosa, M.A.: In: Recami, E. (ed.) Tachyons, Monopoles, and Related Topics. North-Holland, Amsterdam (1978), and references therein

  30. 30.

    Recami, E., Salesi, G.: Phys. Rev. A 57, 98 (1998)

  31. 31.

    Recami, E., Salesi, G.: Adv. Appl. Clifford Algebras 6, 27 (1996)

  32. 32.

    Chodos, A., Hauser, A., Kostelecky, V.: Phys. Lett. B 150 (1985)

  33. 33.

    Jeong, E.J.: Neutrinos must be tachyons. arXiv:hep-ph/9704311

  34. 34.

    Pitkanen, M.: Topological geometro-dynamics. http://tgd.wippiespace.com/public_html/index.html

  35. 35.

    Rodrigues, W. Jr., Maiorino, J.: Random Oper. Stoch. Equ. 4(4), 355 (1996). arXiv:physics/9710030

  36. 36.

    Rodrigues, W.A. Jr., Lu, J.-Y.: Found. Phys. 27, 435–508 (1997)

  37. 37.

    Rodrigues, W.A. Jr., Vaz, J. Jr.: Adv. Appl. Clifford Algebras 7(S), 453 (1997)

  38. 38.

    de Oliveira, E.C., Rodrigues, W.A. Jr.: Phys. Lett. A 296(6), 367 (2001)

  39. 39.

    Santilli, R.M.: Chin. J. Syst. Eng. Electron. 6, 157 (1995)

  40. 40.

    Santilli, R.M.: Elements of Hadronic Mechanics, vols. I and II, 2nd edn. Naukora Dumka, Ukraine Acad. Sci., Kiev (1995)

  41. 41.

    Kehagias, A.: Relativistic superluminal neutrinos. arXiv:1109.6312

  42. 42.

    Alexandre, J., Ellis, J., Mavromatos, N.: On the possibility of superluminal neutrino propagation. arXiv:1109.6296

  43. 43.

    Pavsic, M.: Extra time like dimensions, superluminal motion, and dark matter. arXiv:1110.4754

  44. 44.

    Li, T., Nanopoulos, D.: Background dependent Lorentz violation from string theory. arXiv:1110.0451

  45. 45.

    Lust, D., Petropoulos, M.: Comment on superluminality in general relativity. arXiv:1110.0813

  46. 46.

    Pfeifer, C., Wohlfarth, M.: Beyond the speed of light on Finsler spacetimes. arXiv:1109.6005

  47. 47.

    Li, M., Wang, T.: Mass-dependent Lorentz violation and neutrino velocity. arXiv:1109.5924

  48. 48.

    Tamburini, F., Lavedier, M.: Apparent violation with superluminal Majorana neutrinos at OPERA. arXiv:1109.5445

  49. 49.

    Motl, L.: The reference frame. http://motls.blogspot.com/

  50. 50.

    Contaldi, C.: The OPERA neutrino velocity and the synchronization of clocks. arXiv:1109.6160

  51. 51.

    Haustein, M.: Effects of the theory of relativity in the GPS (2009). http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf

  52. 52.

    Gonzalez, J.F.: A possible explanation of the OPERA experiment based on known well established physics (to appear)

  53. 53.

    Ashby, N.: Relativity in the global positioning system. Living Rev. Relativ. 6, 1 (2003). Available online, http://www.livingreviews.org/Articles/Volume6/2003-1ashby/

  54. 54.

    Thompson, J.: Philos. Mag. 11, 227 (1881)

  55. 55.

    Wanas, M.: Electromagnetic origin of mass. ICTP Trieste preprint IC/87/397

  56. 56.

    Bulyzhenkov, I.: Electromagnetic origin of mass due to folded pseudo-coordinates. arXiv:0810.2062

  57. 57.

    Born, M., Infeld, L.: Proc. R. Soc. London 144(852), 425 (1934)

  58. 58.

    Haeffner, E.: The physical origin of mass and charge. arXiv:physics/0010050

  59. 59.

    Born, M.: Proc. R. Soc. A 165, 291 (1938)

  60. 60.

    Born, M.: Rev. Mod. Phys. 21, 463 (1949)

  61. 61.

    Caianiello, E.: Is there a maximal acceleration? Lett. Nuovo Cimento 32, 65 (1981)

  62. 62.

    Low, S.: J. Phys. A, Math. Gen. 35, 5711 (2002)

  63. 63.

    Low, S.: Nuovo Cimento B 108, 841 (1993)

  64. 64.

    Low, S.: Found. Phys. 36, 1036 (2007)

  65. 65.

    Low, S.: J. Math. Phys. 38, 2197 (1997)

  66. 66.

    Castro, C.: Int. J. Mod. Phys. A 26(21), 3653 (2011)

  67. 67.

    Govaerts, J., Jarvis, P., Morgan, S., Low, S.: Worldline quantization of a reciprocally invariant system. arXiv:0706.3736

  68. 68.

    Vacaru, S.: Superluminal effects for Finsler branes as a way to preserve the paradigm of relativity theories. arXiv:1110.0675

  69. 69.

    Vacaru, S., Stavrinos, P., Gaburov, E., Gonta, D.: Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity. Balkan Press (2006)

  70. 70.

    Miron, R., Hrimiuc, D., Shimada, H., Sabau, S.: The Geometry of Hamilton and Lagrange Spaces. Kluwer Academic, Dordrecht (2001)

  71. 71.

    Castro, C.: Gravity in curved phase-spaces and two-times physics. Int. J. Mod. Phys. A (2011, in press)

  72. 72.

    Brandt, H.: Contemp. Math. 196, 273 (1996)

  73. 73.

    Brandt, H.: Chaos Solitons Fractals 10(2–3), 267 (1999)

  74. 74.

    Girelli, F., Liberati, S., Sindoni, L.: Planck-scale modified dispersion relations and Finsler geometry. Phys. Rev. D 75, 064015 (2007). arXiv:gr-qc/0611024

  75. 75.

    Magueijo, J., Smolin, L.: Gravity’s rainbow. Class. Quantum Gravity 21, 1725–1736 (2004). arXiv:gr-qc/0305055

  76. 76.

    Garattini, R.: Particle propagation and effective spacetime in Gravity’s Rainbow. arXiv:1109.6563

  77. 77.

    Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: D-brane recoil mislays information. Int. J. Mod. Phys. A 13, 1059 (1998). arXiv:hep-th/9609238

  78. 78.

    Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: Quantum gravitational diffusion and stochastic fluctuations in the velocity of light. Gen. Relativ. Gravit. 32, 127–144 (2000). arXiv:gr-qc/9904068

  79. 79.

    Amelino-Camelia, G.: Int. J. Mod. Phys. D 11, 35 (2002)

  80. 80.

    Amelino-Camelia, G.: Int. J. Mod. Phys. D 11, 1643 (2002)

  81. 81.

    Lukierski, J., Nowicki, A., Ruegg, H., Tolstoy, V.: Phys. Lett. B 264, 331 (1991)

  82. 82.

    Amelino-Camelia, G., Gubitosi, G., Loret, N., Mercati, F., Rosati, G., Loret, N.: OPERA-reassessing data on the energy dependence of the speed of neutrinos. arXiv:1109.5172

  83. 83.

    Cohen, A.G., Glashow, S.L.: New constraints on neutrino velocities. arXiv:1109.6562

  84. 84.

    Bi, X., Yin, P., Yu, Z., Yuan, Q.: Constraints and tests of the OPERA superluminal neutrinos. arXiv:1109.6667

  85. 85.

    Chodos, A.: Phys. Today 64(12), 8 (2011)

  86. 86.

    Antonello, M., et al. (ICARUS Collaboration): arXiv:1110.3763

  87. 87.

    Gonzalez-Mestres, L.: Astrophysical consequences of the OPERA superluminal neutrino. arXiv:1109.6630

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Acknowledgements

We thank M. Bowers for her assistance, to Sergiu Vacaru for discussions and to the referee for offering many suggestions to improve the manuscript and pointing out many important references.

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Correspondence to Carlos Castro.

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Castro, C. On Superluminal Particles and the Extended Relativity Theories. Found Phys 42, 1135–1152 (2012). https://doi.org/10.1007/s10701-012-9659-3

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Keywords

  • Extended relativity
  • Clifford spaces
  • Finsler geometry
  • superluminal